What is the limit as x approaches 0 of (1+bx)^{1/x} ?

The limit as x approaches 0 of (1+bx)^{1/x} is e^b

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limit as x approaches 0 of (1+bx)^{1/x}

x \to 0 lim ((1 + b x)^{\frac{1}{x}})

e^{b}

Solution steps

x \to 0 lim ((1 + b x)^{\frac{1}{x}})

Apply exponent rules

= x \to 0 lim (e^{\frac{1}{x} l n (1 + b x)})

Apply the Limit Chain Rule:

e^{b}

= e^{b}

\int t^{2} + \frac{2 t - 1}{t ^{2} - 2 t + 1} d t

x \to - 1 lim (\frac{1}{1 + x ^{2}})

arcsin (9 x + 1)

\int \frac{1}{x ^{\frac{4}{5}}} d x

\int_{2}^{\infty} \frac{1}{x} d x

What is the limit as x approaches 0 of (1+bx)^{1/x} ?
The limit as x approaches 0 of (1+bx)^{1/x} is e^b